Taking Advantage

An Analysis of Advantage/Disadvantage in the D20 System

Mick Cooney

Background

Who Am I?

Dublin Data Science

Goals


Test Intuition


Simulate Mechanisms


Illustrate Typical Examples

Setting Up

Discrete space


No need for simulation


\[\begin{eqnarray*} 1d20 &\rightarrow& 20 \text{ possible outcomes} \\ 2d20 &\rightarrow& 400 \text{ possible outcomes} \end{eqnarray*}\]

Create table of outcomes for 2d20.


\[\begin{eqnarray*} \text{Straight: } &\rightarrow& \text{ use first die} \\ \text{Adv/Disadv: } &\rightarrow& \text{ use max/min of two dice} \\ \text{ROLL(P/M)#: } &\rightarrow& \text{ adjust first die} \end{eqnarray*}\]

d1 d2 Straight Advantage Disadvantage
1 1 1 1 1
1 2 1 2 1
1 3 1 3 1
1 4 1 4 1
1 5 1 5 1
1 6 1 6 1
1 7 1 7 1

Analysing Failure

The Champion


Subclass of Fighter


Critical Hit on 19 or 20

What is the impact of advantage / disadvantage

Roll Type Target Success Prob Failure Prob
Straight 19 0.1000 0.9000
Straight 20 0.0500 0.9500
Advantage 19 0.1900 0.8100
Advantage 20 0.0975 0.9025
Disadvantage 19 0.0100 0.9900
Disadvantage 20 0.0025 0.9975

Opposed Rolls

Resolve Contests


Both Roll 1d20, add bonus

Discrete Space


Bigger and messier


Use simulation

Probabilities Comparison

Examples

1st Level Human Fighter vs Orc Warrior


16 STR / Prof (+5 to roll) -> AC 13


Needs 8 or higher on attack roll

Roll Type Success Failure Failure Ratio
Straight 0.6500 0.3500 1.00
Advantage 0.8775 0.1225 0.35
Disadvantage 0.4225 0.5775 1.65

5th Level Half-Orc Fighter vs Peasant


18 STR / Prof (+7 to roll) -> AC 10


Needs 3 or higher on attack roll

Roll Type Success Failure Failure Ratio
Straight 0.90 0.10 1.0
Advantage 0.99 0.01 0.1
Disadvantage 0.81 0.19 1.9

Unskilled Merchant vs Armored Knight with Shield


10 STR / Not proficient (+0 to roll) -> AC 18


Needs 18 or higher on attack roll

Roll Type Success Failure Failure Ratio
Straight 0.1500 0.8500 1.00
Advantage 0.2775 0.7225 0.85
Disadvantage 0.0225 0.9775 1.15

Summary

+/- 3 on average


Non-linearity


Effects non-intuitive

Thank You!

Other Resources


Stand-Up Maths YouTube Channel


https://www.youtube.com/watch?v=X_DdGRjtwAo


This talk…


https://github.com/kaybenleroll/data_workshops/talk_gaming_dndadv_202301